Elliptic curves over $\Q$ of conductor 3872

Results (18 matches)

  Download displayed columns for results to

Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
3872.a1	3872g1	3872.a	3872g	$1$	$1$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.3.0.1	3Nn	$132$	$12$	$1$	$1$	$1$		$0$	$11520$	$1.171011$	$13824/1331$	$1.17246$	$4.52066$	$[0, 0, 0, 968, -149072]$	\(y^2=x^3+968x-149072\)	3.3.0.a.1, 12.6.0.d.1, 22.2.0.a.1, 66.6.1.a.1, 132.12.1.?	$[]$
3872.b1	3872e1	3872.b	3872e	$1$	$1$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	8.4.0.2		$8$	$4$	$0$	$1$	$1$		$0$	$4224$	$0.977326$	$704$	$0.78666$	$4.16780$	$[0, 1, 0, 1775, -34113]$	\(y^2=x^3+x^2+1775x-34113\)	4.2.0.a.1, 8.4.0-4.a.1.1	$[]$
3872.c1	3872m1	3872.c	3872m	$1$	$1$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$88$	$4$	$0$	$0.357450917$	$1$		$4$	$384$	$-0.221622$	$704$	$0.78666$	$2.42631$	$[0, 1, 0, 15, 31]$	\(y^2=x^3+x^2+15x+31\)	4.2.0.a.1, 88.4.0.?	$[(-1, 4)]$
3872.d1	3872k1	3872.d	3872k	$1$	$1$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$0.312934399$	$1$		$4$	$3840$	$0.772219$	$512/11$	$0.81074$	$3.93758$	$[0, -1, 0, 323, 13301]$	\(y^2=x^3-x^2+323x+13301\)	22.2.0.a.1	$[(59, 484)]$
3872.e1	3872j1	3872.e	3872j	$1$	$1$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1.588579634$	$1$		$2$	$3840$	$0.945024$	$-2515456/11$	$0.85957$	$4.53314$	$[0, -1, 0, -5485, -155131]$	\(y^2=x^3-x^2-5485x-155131\)	22.2.0.a.1	$[(235, 3388)]$
3872.f1	3872b2	3872.f	3872b	$4$	$4$	\( 2^{5} \cdot 11^{2} \)	\( 2^{9} \cdot 11^{6} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-16$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$1440$	$0.581562$	$287496$	$1.17246$	$4.01798$	$[0, 0, 0, -1331, -18634]$	\(y^2=x^3-1331x-18634\)		$[]$
3872.f2	3872b3	3872.f	3872b	$4$	$4$	\( 2^{5} \cdot 11^{2} \)	\( 2^{9} \cdot 11^{6} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-16$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$1440$	$0.581562$	$287496$	$1.17246$	$4.01798$	$[0, 0, 0, -1331, 18634]$	\(y^2=x^3-1331x+18634\)		$[]$
3872.f3	3872b1	3872.f	3872b	$4$	$4$	\( 2^{5} \cdot 11^{2} \)	\( 2^{6} \cdot 11^{6} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.192.9.143	2Cs				$1$	$1$		$3$	$720$	$0.234988$	$1728$		$3.14724$	$[0, 0, 0, -121, 0]$	\(y^2=x^3-121x\)		$[]$
3872.f4	3872b4	3872.f	3872b	$4$	$4$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{6} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓	$2$	16.192.9.178	2B				$1$	$1$		$1$	$1440$	$0.581562$	$1728$		$3.65064$	$[0, 0, 0, 484, 0]$	\(y^2=x^3+484x\)		$[]$
3872.g1	3872h2	3872.g	3872h	$2$	$2$	\( 2^{5} \cdot 11^{2} \)	\( 2^{12} \cdot 11^{3} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$480$	$-0.017912$	$1728$		$2.77989$	$[0, 0, 0, -44, 0]$	\(y^2=x^3-44x\)		$[]$
3872.g2	3872h1	3872.g	3872h	$2$	$2$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{6} \cdot 11^{3} \)	$0$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$1$	$1$		$1$	$240$	$-0.364486$	$1728$		$2.27649$	$[0, 0, 0, 11, 0]$	\(y^2=x^3+11x\)		$[]$
3872.h1	3872a2	3872.h	3872a	$2$	$2$	\( 2^{5} \cdot 11^{2} \)	\( 2^{12} \cdot 11^{9} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$3.180748827$	$1$		$3$	$5280$	$1.181036$	$1728$		$4.52139$	$[0, 0, 0, -5324, 0]$	\(y^2=x^3-5324x\)		$[(-18, 300)]$
3872.h2	3872a1	3872.h	3872a	$2$	$2$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{6} \cdot 11^{9} \)	$1$	$\Z/2\Z$	$\Q(\sqrt{-1})$	$-4$	$N(\mathrm{U}(1))$		✓							$6.361497654$	$1$		$1$	$2640$	$0.834462$	$1728$		$4.01798$	$[0, 0, 0, 1331, 0]$	\(y^2=x^3+1331x\)		$[(625/3, 17650/3)]$
3872.i1	3872c1	3872.i	3872c	$1$	$1$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1$	$1$		$0$	$3840$	$0.772219$	$512/11$	$0.81074$	$3.93758$	$[0, 1, 0, 323, -13301]$	\(y^2=x^3+x^2+323x-13301\)	22.2.0.a.1	$[]$
3872.j1	3872i1	3872.j	3872i	$1$	$1$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$0.910771109$	$1$		$4$	$3840$	$0.945024$	$-2515456/11$	$0.85957$	$4.53314$	$[0, 1, 0, -5485, 155131]$	\(y^2=x^3+x^2-5485x+155131\)	22.2.0.a.1	$[(-15, 484)]$
3872.k1	3872l1	3872.k	3872l	$1$	$1$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.2.0.1		$88$	$4$	$0$	$0.770401319$	$1$		$2$	$384$	$-0.221622$	$704$	$0.78666$	$2.42631$	$[0, -1, 0, 15, -31]$	\(y^2=x^3-x^2+15x-31\)	4.2.0.a.1, 88.4.0.?	$[(5, 12)]$
3872.l1	3872d1	3872.l	3872d	$1$	$1$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	8.4.0.2		$8$	$4$	$0$	$1$	$1$		$0$	$4224$	$0.977326$	$704$	$0.78666$	$4.16780$	$[0, -1, 0, 1775, 34113]$	\(y^2=x^3-x^2+1775x+34113\)	4.2.0.a.1, 8.4.0-4.a.1.1	$[]$
3872.m1	3872f1	3872.m	3872f	$1$	$1$	\( 2^{5} \cdot 11^{2} \)	\( - 2^{12} \cdot 11^{9} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.3.0.1	3Nn	$132$	$12$	$1$	$1$	$1$		$0$	$11520$	$1.171011$	$13824/1331$	$1.17246$	$4.52066$	$[0, 0, 0, 968, 149072]$	\(y^2=x^3+968x+149072\)	3.3.0.a.1, 12.6.0.d.1, 22.2.0.a.1, 66.6.1.a.1, 132.12.1.?	$[]$

  Download displayed columns for results to